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Maths A - Chapter 3

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Maths A - Chapter 3

1. 1. 3 In thisIn this chachapterpter 3A Discount 3B Proﬁt and loss 3C Budgeting 3D Cost of services 3E Credit cards 3F Foreign exchange syllabussyllabusrrefefererenceence Strand: Financial mathematics Core topic: Managing money 1 • Spending money Spending money MQ Maths A Yr 11 - 03 Page 63 Wednesday, July 4, 2001 2:35 PM
2. 2. 64 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d Introduction Karla is now earning better money. Her ﬁrst fortnightly pay of \$985 was deposited into her bank account on Friday, 24 January. Less than two weeks later her account balance was \$28. Karla could not believe that she had spent over \$950. Where did it all go? She sat down and wrote out all the things she had spent money on, and how she had parted with it. Much had been spent at retail stores buying groceries, clothes, books and CDs. She had paid for her purchases in cash. Perhaps, she thought, she should get a credit card, but she found that there were service charges for credit cards, as well as interest. Perhaps she could buy more when there were discounts. She wondered whether she should have a budget. Clearly, she needed a better understanding of the details of handling her hard-earned money, or it was just going to leak away. Discounts, credit card charges, the costs of services and budgeting are topics that affect us all and, like Karla, we owe it to ourselves to understand how these work so that we can make the best use of our money. These and other related topics will be discussed in the following sections of this chapter. 1 Calculate 7.5% of \$450. 2 Increase \$220 by 8%. 3 Reduce \$360 by 15%. 4 After receiving a pay rise of 10%, Jaime’s wage was \$396. What was her wage before the pay rise? 5 Fifty-ﬁve litres of petrol cost \$49. What will sixty litres of petrol cost? SkillS HEET 3.2 SkillS HEET 3.3 SkillS HEET 3.1 MQ Maths A Yr 11 - 03 Page 64 Wednesday, July 4, 2001 2:35 PM
3. 3. C h a p t e r 3 S p e n d i n g m o n e y 65 Discount The ﬁrst thing that Karla decided to do was to get more for her money. Consequently, she decided to buy discounted items wherever possible. A discount is an amount of money by which the price of an item is reduced. If expressed as a percentage of the original price, it is called a percentage discount. Discount = Original price − Sale price Percentage discount = × 100% When the original price and the percentage discount are known, there are two methods of ﬁnding the sale price. Method 1 1. Find the discount in dollars (by ﬁnding the percentage of the original price). 2. Subtract the discount from the original price. Sale price = Original price − percentage of the original price Method 2 1. Treat the original price as 100%. 2. The sale price is then represented by (100% − % discount). Sale price = (100% − percentage discount) of the original price The choice of method depends on the problem. If the problem requires you to ﬁnd the discount in dollars and hence the sale price, use method 1. If the actual amount of a discount is not needed, use method 2 (which gives the sale price straight away). Discount Original price --------------------------------- A vacuum cleaner is discounted from \$180 to \$126. Find the percentage discount. THINK WRITE Find the discount in dollars. Discount = Original price − Sale price = \$180 − \$126 = \$54 Write the formula for the percentage discount. % discount = × 100% Substitute the values of the discount and the original price into the formula and evaluate. % discount = × 100% = 30% Write the answer. The vacuum cleaner was discounted by 30%. 1 2 Discount Original price --------------------------------- 3 54 180 --------- 4 1WORKEDExample MQ Maths A Yr 11 - 03 Page 65 Wednesday, July 4, 2001 2:35 PM
4. 4. 66 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d Sometimes we are given a discount and the sale price and need to ﬁnd the original price, as shown in the following example. Find the sale price on a \$42 kettle after a 12.5% discount has been applied. THINK WRITE Method 1 Find the discount in dollars. Discount = 12.5% of \$42 = × 42 = \$5.25 Find the sale price by subtracting the discount amount from the original price. Sale price = Original price − Discount = \$42 − \$5.25 = \$36.75 Method 2 Express the sale price as a percentage of the original price. Original price = 100%, Discount = 12.5% Sale price = 100% − 12.5% = 87.5% Find the sale price in dollars. Sale price = 87.5% of the original price = × 42 = \$36.75 1 12.5 100 ---------- 2 1 2 87.5 100 ---------- 2WORKEDExample After a 20% discount, a kilogram of scotch ﬁllet steak costs \$9.60. Find the original price and the amount of money saved per kilogram. THINK WRITE Identify the unknown. Let the original price be x. Express the sale price as a percentage of the original price in terms of x. Original price = 100%, Discount = 20% Sale price = Original price − Discount = 100% − 20% = 80% So sale price = 0.8x Form an equation by equating an expression for the sale price with the sale price in dollars and solve for x. 0.8x = 9.60 x = 9.60 ÷ 0.8 = \$12 Find the amount saved. Amount saved = Original price − Sale price = \$12 − \$9.60 = \$2.40 Write the answer. The price of 1 kg of scotch ﬁllet steak before the sale was \$12. The amount of money saved per 1 kg is \$2.40. 1 2 3 4 5 3WORKEDExample MQ Maths A Yr 11 - 03 Page 66 Wednesday, July 4, 2001 2:35 PM
5. 5. C h a p t e r 3 S p e n d i n g m o n e y 67 Discount 1 Find the percentage discount for each of the following items. a A dress, discounted from \$80 to \$60 b A watch, discounted from \$365 to \$185 c A clock, discounted from \$47 to \$34 d A lamp, discounted from \$59 to \$42 e A coffee table, discounted from \$270 to \$239 f A set of kitchen knives, discounted from \$49 to \$36 g A cordless phone, discounted from \$119 to \$89 h A tablecloth, discounted from \$25 to \$18 i A bookshelf, discounted from \$70 to \$63 j A scientiﬁc calculator, discounted from \$30 to \$24 2 Below are some items from a Home Shopper direct marketing brochure. a b c d Next to each item is the retail price and the Home Shopper’s price. For each item, ﬁnd: i the discount amount in dollars when the goods are purchased direct ii the percentage discount. remember 1. Discount = Original price − Sale price 2. Percentage discount = × 100% 3. Sale price = Original price − percentage of the original price = (100% − percentage discount) of the original price Discount Original price --------------------------------- remember 3A WORKED Example 1 MAGIC Blender Blends drinks, sauces, grinds coffee, chops nuts. 12 Month Warranty. Retail \$39.95 Home Shopper’s price \$29.90Home Shopper’s price \$29.90 SANDWICH Toaster Toasted sandwiches to go. Easy clean. 12 Month Warranty. Retail \$29.95 Home Shopper’s price \$22.90Home Shopper’s price \$22.90 TEFLON–Based Iron Light weight, easy glide iron. 12 Month Warranty. Retail \$39.95 Home Shopper’s price \$22.90Home Shopper’s price \$22.90 RETRO–Toaster Your choice of colours, automatic, variable control. 12 Month Warranty. Retail \$39.95 Home Shopper’s price \$32.00Home Shopper’s price \$32.00 MQ Maths A Yr 11 - 03 Page 67 Wednesday, July 4, 2001 2:35 PM
6. 6. 68 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d 3 This advertising brochure states that all manchester (sheets and towels) is discounted by up to 30%. Find the real percentage discount for each item. Comment on your ﬁndings. a Single sheets b Double sheets c Queen sheets d Single quilt cover e Double quilt cover f Queen quilt cover g King quilt cover 4 Healthway is promoting savings in its health and beauty products. For each of the items shown at right, ﬁnd: i the original price ii the percentage discount. 5 Copy and complete the following table. Item Original price (\$) Discount (%) Discount (\$) Sale price (\$) a Microwave oven 300 10% b Furniture set 2030 5% c Mirror 40 30% d Necklace 1560 12.5% e Refrigerator 760 20% f Stereo system 480 33 % g Washing machine 564 25% h Car 7500 50% Health & beauty COSTS LESS at Healthway Health & beauty COSTS LESS at Healthway HAIR COLO URCondtioner Delight Delight & Bright Shampoo Delight Delight& Bright Hair Colour Varieties \$ 957 Save 1.00 Hand cream \$ 545 Save 46c 100s \$ 399 Save 66c 50s \$ 749 Save 86c 75s \$ 1499 Save 2.00 200ml \$ 399 Save up to 99c Vitamin CC Multi Vitamin Horseradish Garlic & a b c d e f WORKED Example 2 1 3 --- MQ Maths A Yr 11 - 03 Page 68 Wednesday, July 4, 2001 2:35 PM
7. 7. C h a p t e r 3 S p e n d i n g m o n e y 69 6 A department store announced a 15% discount on every purchase for one day only. Elena decided to use the opportunity to buy new clothes for her daughter. She bought a dress normally priced at \$29, a 3-piece shorts set (normally \$30), pedal pushers (normally \$16), an embroidered top (normally \$18) and sandals (normally \$26). Find: a the total cost of the clothes b the amount she had to pay after the 15% discount was applied c the amount of money Elena was able to save on these purchases by shopping on that day. 7 The calculation that could not be used to ﬁnd the sale price of a \$64 item after a dis- count of 12.5% is: 8 The ring that will cost \$78 after a discount of 33 % is: A a friendship ring, normally \$104 B a mother of pearl ring, normally \$130 C a sapphire ring, normally \$260 D a Russian band ring, normally \$117 E a ruby ring, normally \$234 9 After a discount of 15%, a jar of Kenya Gold coffee costs \$10.15. Find: a the original price b the amount saved on each jar. 10 A Byer shareholder has a special card which allows a 5% discount on any purchase made at Byer’s supermarkets (excluding items that are already on sale). a What is the total cost of goods purchased by the shareholder who, after producing the card, pays \$166.25. (There are no sale items included.) b What is the amount saved? 11 Before the beginning of a winter sale, a shop assistant was asked to reduce the prices of all items in the store by 12.5%. She calculated the new prices and attached new tags to the goods. At the end of the sale she was asked to put the old prices back. Unfortu- nately, the shop assistant had thrown the old tags away as she did not think she would need them again. She decided to add 12.5% to the sale prices. If the shop assistant proceeds in this manner, will she get back to the original prices? Explain your answer. A B C D of 64 E 64 − × 64 mmultiple choiceultiple choice 12.5 64× 100 ---------------------- 64 12.5 64× 100 ----------------------– 87.5 64× 100 ---------------------- 7 8 --- 1 8 --- mmultiple choiceultiple choice 1 3 --- WORKED Example 3 MQ Maths A Yr 11 - 03 Page 69 Wednesday, July 4, 2001 2:35 PM
8. 8. 70 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d Proﬁt and loss When an item is sold for more than it cost, the difference is said to be proﬁt. It is customary to express proﬁt as a percentage of the cost price: Proﬁt = Selling price − Cost price Percentage proﬁt = × 100% Loss = Cost price − Selling price Percentage loss = × 100% When the cost price and percentage proﬁt/loss are known and we need to ﬁnd the selling price, there are two methods that can be used (see the following example). Profit Cost price ------------------------ Loss Cost price ------------------------ Find the percentage proﬁt on an item that was bought for \$30 and later sold for \$38. THINK WRITE Identify the cost price (CP) and the selling price (SP). CP = \$30; SP = \$38 Write the formula for the proﬁt. (SP > CP) Proﬁt = SP − CP Substitute the values of CP and SP into the formula and evaluate. Proﬁt = \$38 − \$30 = \$8 Write the formula for the percentage proﬁt. Percentage proﬁt = × 100% Substitute the values of proﬁt and CP into the formula and evaluate. Percentage proﬁt = × 100% = 26.67% 1 2 3 4 Profit CP ------------- 5 8 30 ------ 4WORKEDExample Find the percentage loss if an item was bought for \$220 and sold later for \$180. THINK WRITE Identify the cost price (CP) and the selling price (SP). CP = \$220; SP = \$180 Write the formula for the loss. (SP < CP) Loss = CP − SP Substitute the values of CP and SP into the formula and evaluate. Loss = \$220 − \$180 = \$40 Write the formula for the percentage loss. Percentage loss = × 100% Substitute the values of the loss and CP into the formula and evaluate. = × 100% = 18.18% 1 2 3 4 Loss CP ----------- 5 40 220 --------- 5WORKEDExample MQ Maths A Yr 11 - 03 Page 70 Wednesday, July 4, 2001 2:35 PM
9. 9. C h a p t e r 3 S p e n d i n g m o n e y 71 Finally, there are cases when the selling price and the percentage proﬁt (or loss) are known and we need to ﬁnd the CP. The next example shows how to deal with such problems. A shopkeeper buys jumpers from a wholesaler for \$22 each and wants to make a proﬁt of 20% per jumper. What should be the selling price of a jumper to provide this proﬁt? THINK WRITE Method 1 Find the proﬁt in dollars. Proﬁt = 20% of CP = 20% of \$22 = × 22 = \$4.40 Find the selling price by adding the proﬁt to the cost price. SP = CP + Proﬁt = \$22 + \$4.40 = \$26.40 Method 2 Treating the cost price as 100%, express the selling price as a percentage of the CP. CP = 100%; proﬁt = 20% SP = (100 + 20)% = 120% of CP Substitute the values of the CP and substitute. SP = 120% of \$22 = × 22 = \$26.40 1 20 100 --------- 2 1 2 120 100 --------- 6WORKEDExample A retailer sells a TV set for \$732, making herself a proﬁt of 22%. Find the wholesale price of the TV set. THINK WRITE Identify the unknown. Let the CP be x. Express the SP as a percentage of the CP in terms of x. CP = 100% Proﬁt = 22% SP = (100 + 22)% = 122% So SP = 122% of CP = 1.22 × CP = 1.22x Form an equation by making the expression for the selling price equal to \$732. 1.22x = 732 Solve for x. x = 732 ÷ 1.22 x = 600 Write the answer. The wholesale price of the TV set was \$600. 1 2 3 4 5 7WORKEDExample MQ Maths A Yr 11 - 03 Page 71 Wednesday, July 4, 2001 2:35 PM
10. 10. 72 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d Proﬁt and loss 1 Find the percentage proﬁt (to 2 decimal places) for each of the following items. Item CP (\$) SP (\$) a Tracksuit 80 139.95 b T-shirt 16 22.50 c Tennis shoes 49.95 89.95 d Tank top 6 9 e Swimsuit 38 59 f Short socks 2 5.95 g Training pants 20 29 h Tennis skirt 22 36 remember 1. Proﬁt = Selling price (SP) − cost price (CP) 2. Percentage proﬁt = × 100% 3. Loss = CP − SP 4. Percentage loss = × 100% Profit CP ------------- Loss CP ----------- remember 3B Mat hcad Profit and loss WORKED Example 4 MQ Maths A Yr 11 - 03 Page 72 Wednesday, July 4, 2001 2:35 PM
11. 11. C h a p t e r 3 S p e n d i n g m o n e y 73 2 The following goods were sold at a garage sale. Find the percentage loss for each of the items, correct to 2 decimal places. 3 A shopkeeper buys 20 kg of cooking chocolate for \$50 and sells it in 500 g packets at \$3 each. Find the proﬁt made and express it as a percentage of the cost price. 4 Alex had a collection of 5 Betallica CDs, which he purchased over a period of time at \$29.95 each. A friend offered to pay \$70 for the whole set. Find the loss in dollars and express it as a percentage of the cost price. 5 A shopkeeper at the Southbank Markets buys sheepskin moccasins from the wholesaler at the following prices: chil- dren’s sizes — \$12 per pair; adults’ sizes — \$17 per pair, and extra-large sizes — \$19 per pair. If the shopkeeper wants to make a 20% proﬁt, what should be the sale price for each type? 6 Michael buys a car for \$12 000. It depreciates at a rate of \$900 per year. If Michael wants his losses to be no more than 30% of the cost price, after how many years from the purchase does he have to sell the car? 7 By selling a collection of coins for \$177, Igor makes a proﬁt of 18%. What was the original cost of the collection? 8 A retailer has purchased a particular style of jumper which is proving to be unpopular. After attempting to sell them for two consecutive sea- sons, the retailer decides to put them on sale at \$15 each to recover part of the cost. Find the wholesale price of each jumper if the retailer suf- fers a 40% loss. Item CP (\$) SP (\$) a Cutlery 40 8 b Two bedside lamps 100 22 c Vase 35 5 d Toaster 19.95 1.50 e Electric kettle 42 6 f Set of golf clubs 150 45 g Set of building blocks 16 4 h Five paperback books by Sydney Sheldon 60 2.50 WORKED Example 5 WORKED Example 6 WORKED Example 7 MQ Maths A Yr 11 - 03 Page 73 Wednesday, July 4, 2001 2:35 PM
12. 12. 74 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d 1 A tennis racquet is discounted from \$240 to \$180. Calculate the percentage discount. 2 A pair of running shoes is advertised at \$140. What does a customer pay if a 25% discount is applied. 3 After bargaining with the salesperson, Sue has the price of a computer reduced from \$1200 to \$1050. Express this reduction as a percentage of the original price. 4 A carton of drinks is marked at \$28. If all stock is reduced by 15%, calculate the cost of the drinks. 5 A shopkeeper buys a 12-kg case of tomatoes for \$20. If he sells all of the tomatoes for \$2.50 per kg, calculate the percentage proﬁt. 6 Karen pays \$12 each for fake name brand watches. When she sells them she wants to make an 80% proﬁt. What price should she sell these watches for? 7 Michelle buys and sells second-hand skateboards. She makes a 40% proﬁt on each sale. If she sells a skateboard for \$56, what did she originally pay for the skateboard? 8 John paid \$50 for a dozen trophies. If he sells them for \$14 each, calculate the per- centage proﬁt. 9 P-Mart make 30% on all their sales. If they pay \$600 for a dining suite, what price should they sell it for to make the desired proﬁt? 10 Hans sells a restaurant for \$198 000. He calculates that he has made a 10% proﬁt on the buying price. What did he pay for the restaurant originally? Dealing in diaries Just before Christmas a shopkeeper purchased a box of 50 diaries for \$120. 1 Find the cost price of each diary. 2 If he sold 30 diaries before Christmas at \$5 each, calculate the proﬁt that he would make. 3 Find the percentage proﬁt. 4 If, after Christmas, the shopkeeper sold the remaining diaries for \$1 each, ﬁnd the percentage loss on each of these diaries. 5 After the shopkeeper had sold the leftover diaries (at \$1 each), ﬁnd the total proﬁt that he made. 6 Express the total proﬁt as a percentage of the cost price. 7 Find the proﬁt that the shopkeeper could have made had he managed to sell all of the diaries before Christmas (at \$5 each). 8 What was his loss (in dollars) by not selling all of his diaries before Christmas? 9 Express the loss as a percentage of the potential proﬁt. 1 inv estigat ioninv estigat ion MQ Maths A Yr 11 - 03 Page 74 Friday, July 6, 2001 1:56 PM
13. 13. C h a p t e r 3 S p e n d i n g m o n e y 75 Budgeting Karla wants to go to New Zealand for her holidays next year; but if she saves only \$28 each pay, she will certainly not have enough money to go. Although she is to receive a pay rise, she realises that she still does not know how much she will need to save. She understands that a budget will help her, so decides to look into the principles of budgeting in more detail. A budget is a table containing an estimate of income and expenditure. A personal (or family) budget can help you to: 1. ensure that you do not spend more than you earn 2. estimate the amount of money that you can save 3. control your expenses and perhaps cut some of them in order to save more 4. decide what you can and what you can’t afford. A personal budget helps you to make various ﬁnancial decisions. The expenses in the personal (or family) budget can be divided into two major categories: ﬁxed (or unavoidable) expenses and variable expenses. Fixed expenses may include rent or mortgage, medical insurance, car regis- tration and other regular payments that must be paid and can’t be varied. Variable expenses include food, entertainment, clothing and other items that can be controlled or varied. To reduce some expenses in order to save more money, one would look into variable expenses. A weekly, monthly or yearly budget can be prepared. Expenses may be weekly (such as food), monthly (health insurance), quarterly (electricity bills) or yearly (car registration). Depending on the budget duration, all expenses should be converted to weekly, monthly or yearly amounts. The following table of conversion is helpful in budget preparation. It should be understood that budgets give only an approximation of the real-life situation, as they are based on estimates and do not include unexpected expenses. Purpose Convert from Convert to Operation Weekly budget Monthly cost Weekly cost × 12, then ÷ 52 Yearly cost Weekly cost ÷ 52 Monthly budget Weekly cost Monthly cost × 52, then ÷ 12 Yearly cost Monthly cost ÷ 12 Yearly budget Weekly cost Yearly cost × 52 Monthly cost Yearly cost × 12 MQ Maths A Yr 11 - 03 Page 75 Wednesday, July 4, 2001 2:35 PM
14. 14. 76 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d Karla’s monthly budget. Use the table to resolve each of the following. a Calculate the total of the ﬁxed expenses. Note that Karla views health insurance, house contents insurance and car insurance as important expenses, and their regular pay- ments are ﬁxed. b Calculate the total of the variable expenses. c Calculate the amount available for saving. d If Karla wishes to take a vacation and travel to New Zealand (estimated cost \$3500), for how long does she have to save? e Suggest some possibilities for cutting expenses in order to save enough money for the New Zealand holiday one month sooner. Income Expenses Salary after tax \$2050 Dividends from shares \$23 Rent of 1-bedroom ﬂat \$520 Electricity \$70 Phone \$40 Health insurance \$30 House contents insurance \$10 Car registration \$27 Car insurance \$42 Petrol \$35 Food \$110 Clothing \$150 Entertainment \$150 Sport \$100 Miscellaneous \$40 Total: \$2073 Total: \$1324 THINK WRITE a Identify the ﬁxed expenses and add them up. a Fixed expenses: Rent \$520 Health insurance \$30 House contents insurance \$10 Car registration \$27 Car insurance \$42 Total = 520 + 30 + 10 + 27 + 42 = \$629 b Calculate the total of variable expenses by subtracting ﬁxed expenses from the total. b Total of variable expenses = total expenses − total of ﬁxed expenses = 1324 − 629 = \$695 c Calculate monthly savings by subtracting expenses from the income. c Monthly savings = monthly income − monthly expenses = 2073 − 1324 = \$749 8WORKEDExample MQ Maths A Yr 11 - 03 Page 76 Wednesday, July 4, 2001 2:35 PM
15. 15. C h a p t e r 3 S p e n d i n g m o n e y 77 The Australian budget Budgets can be prepared for individuals, families and small organisations. However, there is also a budget for each country. Investigate the last Australian budget. 1 Who prepares the budget? 2 What is the budget’s period? 3 What is/are the source/s of income? 4 What are the items in the expenditure section (that is, where does the money go)? 5 Was there any deﬁcit in the last budget? THINK WRITE d Calculate the number of months required to save for the holiday. d To save \$3500 at the rate of \$749 per month: 3500 ÷ 749 = 4.67 or approximately 5 months e Identify the number of months within which the money is to be saved. e To save one month sooner than calculated in part d means 5 − 1 = 4 months Calculate the amount required to be saved monthly. Monthly savings needed = 3500 ÷ 4 Monthly savings needed = \$875 Calculate the extra amount which is to be saved per month. Extra monthly savings needed = \$875 − \$749 = \$126 Suggest cuts in variable expenses. Cuts could be made as follows: Phone bills: cut from \$40 to \$30 gives \$10 Clothing: cut from \$150 to \$80 gives \$70 Entertainment: cut from \$150 to \$104 gives \$46 This gives 10 + 70 + 46 = \$126, which is the required extra saving. 1 2 3 4 inv estigat ioninv estigat ion remember 1. A budget is a table that contains an estimate of income and expenditure. 2. The two major categories of expenses are ﬁxed and variable expenses. 3. Both budget and expenses can be calculated weekly, monthly, quarterly or yearly. Depending on the budget, all expenses should be recalculated for the same time interval. remember MQ Maths A Yr 11 - 03 Page 77 Wednesday, July 4, 2001 2:35 PM
16. 16. 78 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d Budgeting 1 The table below shows the monthly budget for a couple with one school-aged child. Use the table to calculate the following: a the total of ﬁxed expenses b the total of variable expenses c the total monthly savings d the time needed for the family to save enough for a trip to Bali (estimated cost \$3000). 2 List as many variable expenses as you can that are missing from the budget in question 1. 3 A university student who lives with her parents has the following expenses: she pays her parents \$50 per week for board and food; a monthly ticket for public transport costs her \$63; she spends on average \$40 a month on books and stationery; her single health insurance premium is \$24 a month; entertainment and snacks cost her about \$55 a month; the university enrolment fee takes \$300 a year and she also needs clothes and accessories which cost approximately \$15 per week. a Prepare a monthly budget if the student’s income consists of Austudy (which is \$116 per week) plus birthday and Christmas presents (\$250 a year). b Calculate the amount of money that she can save per month. Income Expenses Combined monthly salary after tax \$3800 Mortgage repayments \$1200 Rates \$75 Building insurance \$20 Contents insurance \$15 Electricity \$120 Gas \$25 Telephone \$50 Car registration \$35 Car insurance \$50 Health insurance \$60 School fees \$110 Food \$160 Clothing \$60 Entertainment \$100 Sport \$75 Miscellaneous \$120 Household needs and repairs \$20 Petrol \$55 Total: \$3800 Total: \$2350 3C WORKED Example 8 MQ Maths A Yr 11 - 03 Page 78 Wednesday, July 4, 2001 2:35 PM
17. 17. C h a p t e r 3 S p e n d i n g m o n e y 79 4 Using the ﬁgures in the table below, prepare an expenditure side of a weekly budget. 5 The student in question 3 is offered a part-time job in the university cafeteria, where she will be able to earn \$66 per week. a Calculate her total monthly savings if she accepts this position. b Our student is considering moving in with her friends. By doing so she will save the \$50 per week that she is paying to her parents in board and food, but she will have to pay \$100 per month for her share of the rent. She will also have to contribute \$45 per month for electricity and phone bills and \$60 per week for food. With the new job can the student afford to move out of home? Support your answer with appropriate calculations. 6 Prepare your personal monthly budget (or your family budget if you do not have any income). Are there any possibilities for cutting some of the expenses? 7 Members of a welfare group are discussing the budget for the next year. Their income will come from three sources: a government subsidy of \$4200; annual membership fees of \$25 per person and proﬁts from the various events. They estimate that the auction will bring in \$400, proﬁts from the food stalls (at the picnic and the three local fairs) will be \$230 each time and proﬁts from the two concerts will yield about \$1800 each. They also estimate that about 650 people will renew their membership. The money will be spent as follows: rent of the premises at \$500 a month; publishing the newsletter \$240 per quarter; expenses of \$180 associated with each Sunday School for 40 weeks a year; electricity and phone bills at \$220 a month; public liability and contents insur- ance, \$1860 per year. Advertising will cost \$30 per month and stationery \$250 per year. After buying a new computer (for about \$3500) and allowing \$2000 for unexpected expenses, the rest of the money will be spent on charity. a Prepare a yearly budget for the welfare group. b Calculate the amount of money left to use for charity. c Express your answer to b as a percentage of the annual income. Item Cost and period Rent \$600 per month Food \$90 per week Electricity \$420 per 3 months Gas \$40 per 2 months Phone \$360 per 3 months Car registration \$430 per year Car insurance \$500 per year Health insurance \$175 per 3 months Contents insurance \$125 per year Clothes \$100 per month Entertainment \$80 per month Work SHEET 3.1 MQ Maths A Yr 11 - 03 Page 79 Wednesday, July 4, 2001 2:35 PM
18. 18. 80 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d Cost of services An important part of being able to prepare a personal budget is to understand how various organisations charge for their services. The following questions are designed to help you investigate the cost of services, such as electricity and gas charges, water and council rates and the costs of using a telephone. The club’s end-of-season break-up Work in groups of three. Karla is a member of the committee of her local netball club and she has been asked to organise food and drinks for the club’s breakup. It is to be a BBQ held at the club grounds. Everyone who attends will be asked to pay a certain amount and the club will supply food and drinks. Last year about 100 people attended and the number is expected to be the same this year. Your task: 1 Help Karla plan a menu, indicating what each person could be expected to eat and drink. 2 Prepare a shopping list with deﬁnite, speciﬁc quantities and prices. 3 Suggest to the committee a cost per person that should cover expenses plus 10%. investigat ioninv estigat ion MQ Maths A Yr 11 - 03 Page 80 Wednesday, July 4, 2001 2:35 PM
19. 19. C h a p t e r 3 S p e n d i n g m o n e y 81 Cost of services Study the electricity bill shown below and answer the following questions. 1 a What is the total amount to be paid? b When should this bill be paid? c How does this bill compare with the bill from the previous quarter? d On what dates were the meter readings taken? e What is the average daily cost of electricity? f If the Beales want to prepare a weekly budget, what amount should they allocate to the cost of electricity? g How does the average daily kWh usage compare with the same period last year? 2 The bill records two different types of consumption — Tariff 11 (used for lights, toasters etc.) and Tariff 33 (used for hot water systems and other devices whose power consumption can be restricted to off-peak times). 3D MQ Maths A Yr 11 - 03 Page 81 Wednesday, July 4, 2001 2:35 PM
20. 20. 82 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d a How many kWh in Tariff 11 were used in the quarter? b What was the most recent Tariff 11 meter reading? c What GST was charged on the Tariff 11 consumption? d What is the cost of the Tariff 11 supply before GST is added? e Calculate the cost of Tariff 11 supply (in cents per kWh) if it is charged at a ﬂat rate. 3 a Estimate the consumption, in kWh, of Tariff 11 supply for the February quarter account last year. b Estimate the consumption, in kWh, of Tariff 33 supply for the February quarter account last year. c Estimate the cost of last year’s bill, if the rates charged were the same as those charged this year. (Include GST.) 4 Study the gas bill shown below for the February quarter and answer the following questions. MQ Maths A Yr 11 - 03 Page 82 Wednesday, July 4, 2001 2:35 PM
21. 21. C h a p t e r 3 S p e n d i n g m o n e y 83 a What is the value of the bill? b How does this bill compare with last quarter’s? c How does this bill compare with the bill for the same quarter last year? d What is the average daily cost of gas consumption? e What would you estimate the yearly cost of gas consumption? f If Jane is to make a monthly budget, how much should she allow for gas? 5 The following ﬁgure shows the reverse side of the gas bill. You will notice that the amount of gas consumed is given in Megajoules (MJ) and is calculated indirectly from the meter readings. An ‘MJ factor’, which depends on quantities such as temperature and pressure, is used to convert from the meter read- ings to Megajoules. a What is the difference between the meter readings? b Explain how the consumption, in MJs, is calculated from the difference between meter readings. c How much GST is charged in this bill? d What is the rate, in cents per MJ, of the cost of the ﬁrst 1710 MJ? e Using the rates given in the bill, calculate the cost of 6000 MJ (excluding GST). 6 In the May quarter last year the average daily consumption of gas was 70 MJ. If there were 91 days in this quarter, calculate the: a total gas consumption for the quarter b total cost of this gas (excuding GST) c GST payable on this cost of gas d total cost of gas for this quarter. 7 In the August quarter last year the average daily consumption of gas was 85 MJ. If there were 93 days in this quarter, determine the total cost of gas for this quarter, including GST. MQ Maths A Yr 11 - 03 Page 83 Wednesday, July 4, 2001 2:35 PM
22. 22. 84 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d Questions 8 to 11 refer to the Brisbane City Council Rates notice shown below. MQ Maths A Yr 11 - 03 Page 84 Wednesday, July 4, 2001 2:35 PM
23. 23. C h a p t e r 3 S p e n d i n g m o n e y 85 8 a What amount is to be paid, if the bill is paid before 13th June? b What amount is to be paid, if the bill is paid after 13th June? c Why is Mr Ratepayer’s bill subsidised? d Calculate the bill to be paid if the subsidies and remissions were not given. e Estimate Mr Ratepayer’s yearly rates bill. f If he is planning a monthly budget, how much should he allocate for rates? 9 a How much water is used in the quarter? b What is the cost, in cents per kL, of water? c How much water would he expect to use in a year? MQ Maths A Yr 11 - 03 Page 85 Wednesday, July 4, 2001 2:35 PM
24. 24. 86 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d 10 If Mr Ratepayer’s water meter readings were 845 987 calculate his water bill for this period. Include the water service charge. 11 a What was the increase in the valuation of the property from 01 July 1998 to 01 July 1999? b Express this increase as a percentage of the original valuation. 12 The ﬁrst page of a telephone bill issued by Telstra is shown below. a Explain how the total of this bill was calculated from the components shown. b What percentage of the total bill does the service charge represent? c Is there any concession available for the telephone bill? d If the service charge is always constant, what was the total of the previous bill, assuming that the Flexi-Plan was not yet introduced? Telstra Bill Telstra Corporation Limited ACN 051 775 556 Account number Opening Balance We received 93 G Flexi-Plan balance 8.40cr 91 G Call charges to 23 June 116.51 92 G Service and equipment to 23 June 42.45 Total of this bill \$150.56 Item Account Summary Your Reference 07 5551 0000 \$ Balance Total of this bill Bill number Date of issue Bill enquiries Total amount payable \$150.55 30 Jun 01 Payment to be made by T 000 123 123-2 \$0.00 MS A SAMPLE 10 SAMPLE STREET SAMPLEVILLE 0000 \$0.00 \$0.00 \$150.56 000 0000 034 25 June 01 13 20 00 Calling Patterns Compared With Last Bill Local Calls up by \$8.75 STD Calls up by \$4.06 Calls to Mobiles up by \$2.00 June-00 Oct-00 Mar-01 June-01 \$200 \$160 \$120 \$80 \$40 \$0 Same Time Last year Total Bill MQ Maths A Yr 11 - 03 Page 86 Wednesday, July 4, 2001 2:35 PM
25. 25. C h a p t e r 3 S p e n d i n g m o n e y 87 13 Page 3 of the Telstra bill is shown below. a According to the service summary, how many metered calls were made and what was the cost of each call? b What percentage of the service and equipment charge does the rent of the telephone represent? c If a family buys a telephone valued at \$89 and hence stops renting one from Telstra, in how many months will the savings from not paying rental cover the cost of the new phone? d Use the itemised STD Calls section to ﬁnd the afternoon rate for calling Marysville. e Study the Calls Direct to Mobiles itemised section and complete the following statement: ‘Judging from the bill it is reasonable to assume that the off peak rate is applied to any calls to mobiles made after pm.’ Local Call Saver 15 69 Plan fee 23 Mar to 23 June 0.00 71 Discount 8.40 cr Plan balance \$8.40 cr Total Flexi-Plan balance \$8.40 cr Item Flexi-Plan Details \$ Telephone Service 07 5551 0000 Flexi-Plan/Concession discounts \$8.40 cr Call charges 51 Metered calls 23 Mar to 23 June 404 units at \$0.25 each 101.00 57 STD to 23 June 8 calls 6.51 58 Calls direct to Mobiles to 23 June 9 calls 9.00 Service and equipment 2 1 Telephone Handset Rental Rent in advance 23 Mar to 23 June 2.50 7.50 1 1 Telephone Line Rental Rent in advance 23 Mar to 23 June 11.65 34.95 Total for 07 5551 0000 \$150.56 Item Service Summary \$ STD Calls Date Time Place Number Rate Min:Sec \$ Telephone Service 07 5551 0000 27 23 Mar 02:54 pm Marysville 03596 Afternoon 2:30 0.57 25 23 Mar 08:13 pm Warburton 03585 Economy 1:51 1.28 26 23 Mar 06:54 pm Marysville 03596 Economy 1:05 0.23 24 02 Apr 03:32 pm Marysville 03596 Economy 1:35 0.28 21 03 Apr 01:04 pm Warburton 03585 Afternoon 2:39 1.48 22 02 May 10:01 pm Marysville 03596 Economy 1:09 0.24 19 07 May 02:17 pm Warburton 03585 Economy 4:12 1.54 20 09 May 10:34 am Marysville 03596 Economy 7:42 0.89 STD Calls Date Time Place Number Rate Min:Sec \$ Telephone Service 07 5551 0000 45 23 Mar 08:13 pm Mobile 0411309 Off Peak 0:17 0.50 46 23 Mar 04:39 pm Mobile 0411309 Peak 0:47 1.25 48 06 Apr 12:33 pm Mobile 0411309 Peak 0:42 1.00 47 10 May 02:59 pm Mobile 0411309 Peak 0:43 1.00 50 07 May 01:33 pm Mobile 0411309 Peak 1:44 1.25 44 08 May 12:35 pm Mobile 0411834 Peak 4:19 2.25 49 21 May 08:37 am Mobile 0411309 Off Peak 0:07 0.50 37 23 Mar 06:42 am Mobile 0411309 Peak 0:20 0.50 43 03 May 07:36 pm Mobile 0411690 Off Peak 0:36 0.75 Item Item STD Calls - Itemised \$ Calls To Mobiles - Itemised \$ Page 3 MQ Maths A Yr 11 - 03 Page 87 Wednesday, July 4, 2001 2:35 PM
26. 26. 88 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d Credit cards Karla has decided that it is time for her to obtain a credit card. A credit card will allow her to purchase goods and services without paying for them on the spot. They can also be used for obtaining cash advances, paying bills and making purchases over the phone or on the Internet. Common credit cards used in Australia include MasterCard, Visa, Bankcard, Diners Club and American Express. When applying for a MasterCard, Visa or Bankcard, a customer is given a choice of having either an interest-free period (usually up to 55 days) for a small annual fee (around \$22), or no fee payable and no interest-free period (with the interest rate usually being lower for the second option). Each cardholder is offered a certain limit of credit. A monthly statement showing all transactions for the previous month is issued for every cardholder. Upon receiving a monthly statement, a customer may decide to pay the bank in full by the due date indicated on the statement and hence not have to pay any interest with an interest-free period card. Alternatively, the customer may choose to make the minimum payment only. In this case interest will be charged on the unpaid balance. The minimum payment is usually a certain percentage of the unpaid balance or a certain ﬁxed amount — whichever is larger. Variations in interest rates occur from time to time and cardholders are notiﬁed of these changes in advance. Below are two extracts from Commonwealth Bank brochures outlining part of their credit policy. Source: Commonwealth Bank. Credit Cards — Check Out Our Credit Card Advantages. Valid as at 10 May 2001. Statement of the cost of credit: In accordance with section 158(1)(b) of the Consumer Credit Code, we make the following statement of the cost of credit for the purposes of section 140(3) of that Code: As at 10 May 2001, the annual percentage rates for our standard credit cards are: MasterCard/Visa/Bankcard 15.90% (up to 55 interest free days with an annual fee) MasterCard/Visa/Bankcard 14.25% (no interest free days with no annual fee) Fees and charges are payable. The above annual percentage rates may change. Please call us on 13 2221 from 8am to 8pm, Monday to Friday, or ask at any branch for our up-to-date rates. MQ Maths A Yr 11 - 03 Page 88 Wednesday, July 4, 2001 2:35 PM
27. 27. C h a p t e r 3 S p e n d i n g m o n e y 89 Source: Commonwealth Bank. Credit Cards — Conditions of Use — Valid as at 04/01. Subject to change. For the ‘No interest-free period’ option the interest charged on the outstanding amount of each purchase and cash advance is charged from the date of the purchase (or cash Gold MasterCard, Visa Gold On some Gold card accounts we may require a minimum payment each month whilst on others we may require a minimum payment once each six months. Monthly minimum payments If a statement of your card account shows a closing balance of less than \$25, the minimum payment is the closing balance. Otherwise, the minimum payment you must make is the greatest of: • the excess of the closing balance over the credit limit on your card account; • 1.5% of the closing balance (rounded down to the nearest dollar if the closing balance of your card account is \$1,700 or more); or • \$25. Find the minimum payment due for each of the following balances using the information supplied previously. a \$23.40 b \$1236.25 c \$280.10 d \$1560 with the credit limit being \$1500 THINK WRITE a Since the closing balance is under \$25, it should be paid in full. a As \$23.40 < \$25, the amount due = \$23.40 b Since the closing balance is over \$1000, calculate 2.5% of it. b Amount due = 2.5% of \$1236.25 = × 1236.25 = \$30.91 Round down to the nearest dollar. Rounded down to the nearest dollar, the amount due is \$30. c Since the closing balance is above \$25 but below \$1000, the minimum payment is \$25. c \$25 < \$280.10 < \$1000 Therefore payment due = \$25 d Since the closing balance is above \$1000, calculate 2.5% of it and round down to the nearest dollar. d 2.5% of \$1560 = × 1560 = 39 Calculate the excess of the closing balance above the credit limit. The excess of the closing balance above the credit limit = \$1560 − \$1500 = \$60 Select the greater of the two amounts. As \$60 > \$39, the amount due is \$60. 1 2.5 100 --------- 2 1 2.5 100 --------- 2 3 9WORKEDExample MQ Maths A Yr 11 - 03 Page 89 Wednesday, July 4, 2001 2:35 PM
28. 28. 90 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d advance) and until the purchase (or cash advance) is repaid in full. The same is true for cash advances, obtained with ‘55 days interest-free period’ cards. An extract from the Commonwealth Bank brochure explains the procedure. Source: Commonwealth Bank. Credit Cards — Conditions of Use — Valid as at 04/01. No interest-free days cards We charge interest on the outstanding amount of each purchase, permitted transaction and cash advance from the date the purchase, permitted transaction or cash advance is debited to your card account until you repay the purchase, permitted transaction or cash advance. We calculate interest for a statement period in three steps: • first, we average the outstanding balances over the statement period; • then we multiply the average by the daily percentage rate applying to your card account; and • finally, we multiply the result we get from the prior step by the number of days in the statement period. The result we get from the last step is the amount of interest we charge to your card account in the statement period. When do we debit interest? We debit your card account on the last day of each statement period with the interest we calculated during that statement period up to and including that last day. For a ‘no interest-free period’ credit card, calculate the interest charged on the average outstanding daily balance of \$220 with the interest percentage rate of 13.95% p.a. if the statement covers a 30-day period. THINK WRITE Calculate the daily percentage rate. Daily % rate = = = 0.038 22 Calculate the daily interest charged on the outstanding balance. Interest = 220 × = 0.084 08 Find the interest charged over the 30-day period and round-off to the nearest cent. Total interest for 30 days = 0.084 08 × 30 = 2.522 47 = \$2.52 (to the nearest cent) 1 annual % rate 365 --------------------------------- 13.95 365 ------------- 2 0.038 22 100 -------------------- 3 10WORKEDExample MQ Maths A Yr 11 - 03 Page 90 Wednesday, July 4, 2001 2:35 PM
29. 29. C h a p t e r 3 S p e n d i n g m o n e y 91 For ‘up to 55 days interest free’ credit cards, no interest is charged if the amount is paid in full by the due date which is usually 25 days from the date of the statement. If the closing balance is not repaid in full by the due date, the cardholder then temporarily loses the interest-free option. The interest is usually charged on the outstanding balance from the day of the ﬁrst purchase (that is, it is backdated!) until the outstanding balance is paid in full. Any purchases made before the balance is fully repaid are also added to the total. So basically if the balance is not paid in full by the due date, the card is effectively a ‘no interest-free period’ card, but with the higher interest rate being applied. For a ‘55 days interest free’ credit card, calculate the amount of interest charged on an outstanding balance of \$450 which was repaid 10 days after the due date, given that the ﬁrst purchase was made on the ﬁrst day of the 30-day statement period and the annual percentage interest rate was 15%. (Assume that no other purchases were made after the end of the statement.) THINK WRITE Calculate the length of time for which the interest is charged, keeping in mind that it is charged from the date of the ﬁrst purchase and until the balance was repaid. The number of days from the ﬁrst purchase to the last day of statement = 30 (as the purchase was made on the ﬁrst day and the period covers 30 days). The number of days from the date of the state- ment to the due date = 25. The number of days from the due date to the date of actual payment = 10. Total days = 30 + 25 + 10 = 65 Calculate the daily interest rate. Daily interest rate = = 0.041 096 Find the interest charged on \$450 over the period of 65 days and round-off to the nearest cent. Interest = \$450 × × 65 = \$12.02 1 2 15% 365 ----------- 3 0.041 096 100 ----------------------- 11WORKEDExample remember 1. The two options for Visa, MasterCard or Bankcard are: (a) no annual fee and no interest-free period (b) an annual fee and a speciﬁc interest-free period. 2. The bank requires a minimum monthly payment which is usually the greater of a certain ﬁxed amount or a speciﬁc percentage of the closing balance. 3. For all transactions made with a ‘no interest-free period’ card and for cash advances obtained with an ‘up to 55 days interest-free period’ credit card, the interest is calculated from the date of the ﬁrst purchase. 4. For interest-free period credit cards, if the closing balance is paid in full by the due date indicated on the statement, no interest is incurred. Otherwise, interest is charged until the balance is repaid. remember MQ Maths A Yr 11 - 03 Page 91 Wednesday, July 4, 2001 2:35 PM
30. 30. 92 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d Credit cards 1 The XYZ Bank requires the minimum payment off credit card balances to be: (a) the closing balance if it is under \$25, or (b) the greatest of: ii(i) the excess of the closing balance over the credit limit, or i(ii) 2.5% of the closing balance (rounded down to the nearest dollar), or (iii) \$25. Calculate the minimum payments on each of the following balances. a \$17.50 b \$26.49 c \$147.42 d \$785.00 e \$1326.12 f \$2312.58 g \$3489.60 h \$1954.00 with a limit of \$1900 i \$2320.48 with a limit of \$2300 j \$3080.00 with a limit of \$3000 2 For a ‘no interest-free period’ credit card, calculate the interest charged on an average outstanding daily balance of \$430 with a percentage interest rate of 14.01% p.a. if the statement covers a 30-day period. 3 An ‘up to 55 days interest free’ credit card holder used his card on 15 March to obtain a cash advance of \$365, which he repaid on 20 March. What was the amount of interest charged on the cash advance at the rate of 15.01% p.a.? 4 Here is some information extracted from a monthly credit card statement: Statement begins: 1 April; Statement ends: 30 April; Payment due date: 25 May Date Transaction Details Amount 03 Apr HBA 180.00 08 Apr Myer Indooroopilly 89.00 16 Apr Optus 252.25 22 Apr Coles Fairﬁeld 112.90 30 Apr Sportsgirl City 69.95 a Calculate the interest-free period for each of the above transactions. b Complete the following sentence: ‘To make full use of the “up to 55 days interest free” option, the purchases should be made at the of the statement period’. 5 For a ‘55 days interest free’ credit card, calculate the amount of interest charged on an outstanding balance of \$625 which was repaid a fortnight after the due date, given that the ﬁrst purchase was made on the ﬁrst day of the 30-day period and the annual percentage rate was 14.98%. (Assume that no other purchases were made after the end of the statement in question.) 6 Study the statement for the ‘55 days interest-free period’ credit card which follows and answer these questions. a What is the length of the period of time covered by this statement? b What was the closing balance of the previous statement? 3E WORKED Example 9 WORKED Example 10 WORKED Example 11 MQ Maths A Yr 11 - 03 Page 92 Wednesday, July 4, 2001 2:35 PM
31. 31. C h a p t e r 3 S p e n d i n g m o n e y 93 c Did the payment of the previous statement balance incur any interest charges? Explain your answer. d Explain how the minimum amount due was calculated. e Explain how the amount of available credit was calculated. 7 The closing balance for the statement in question 6 was repaid in full on 20 June. Find the amount of interest charged, if: a no further purchases were made until that date b a further \$300 was spent on 31 May. Date 29 Apr 30 Apr 3 May 8 Apr 4 May 4 May 5 May Reference Number 74900052MENTAJ 89101123XYZ FIZ3456ROGERDUTY 72345670J4U00ABCD 12345678GOODILUV 789108ABCD1234 7654321XYZWRST MS ILA NORMAN 32 BROWN STREET BUNDABERG Q 4670 MS ILA NORMAN Transaction Details Payment received - thank you Interest charges Goverment duties - last month Travel Wide Melbau Books & Musical World Carlton AU SCUD Shoes Noble Park AU Groovy Music Nth Mlbourne AU Amount (A) \$ 22.10- 2.50 0.32 296.18 47.00 128.00 176.00 2345 6789 1234 9299 1 OF 1 2345 6789 1234 9299 \$0.00 \$22.10 + \$650.00 - \$22.10 + \$650.00 Overdue/Over limit Opening Balance Available credit \$350 Credit limit \$1000 Daily percentage rate .04136 Annual percentage rate 15.100 New charges Payments/refunds Closing Balance 8 APRIL 2001 5 MAY 2001 30 MAY 2001 30 MAY 2001 SPECIMEN STATEMENT ONLY – USED FOR PURPOSE OF ILLUSTRATION. Valid as at 05/01. MQ Maths A Yr 11 - 03 Page 93 Wednesday, July 4, 2001 2:35 PM
32. 32. 94 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d TAXI The exchange rate When Karla visits New Zealand she will not be able to use Australian currency (for example to hire a taxi or buy food). She ﬁrst has to convert Australian dollars (A\$) to New Zealand dollars (NZ\$). How many NZ\$ can she buy with one A\$? This varies from day to day according to what is called the exchange rate. A table showing exchange rates for all major currencies is shown below. Karla takes her Australian currency to a bank (preferably after prior arrangement) and they will sell her New Zealand dollars. Using the table above, we see that they will sell her NZ\$1.2659 for every A\$1 she hands over. YOUR DOLLAR Buying Selling \$1A eq: \$ US .............................. 0.5885............. 0.5829 \$1A eq: £ Sterling ....................... 0.3897............. 0.3827 \$1A eq: Austrian schil..................... 8.74................. 8.52 \$1A eq: \$ Canada....................... 0.8691............. 0.8500 \$1A eq: Danish Krone................. 4.7340............. 4.8174 \$1A eq: EUR............................... 0.6346............. 0.6196 \$1A eq: \$ Fiji............................... 1.2483............. 1.1935 \$1A eq: Finland Markka.............. 3.7729............. 3.6852 \$1A eq: French franc .................. 4.1624............. 4.0657 \$1A eq: Ger. d-mark ................... 1.2412............. 1.2122 \$1A eq: Greek drachma.............. 213.92............. 208.59 \$1A eq: \$ Hong Kong ................. 4.6236............. 4.5094 \$1A eq: India r’pee.................... On App............On App. \$1A eq: Indonesia r/piah............. 5364.0............. 4885.0 \$1A eq: £ Ireland ........................ 0.4998............. 0.4881 \$1A eq: Italian lira....................... 1229.0............. 1199.0 \$1A eq: Japan yen........................ 64.37............... 63.13 \$1A eq: Malay ringgit................ On App............On App. \$1A eq: New Taiwan \$.................. 18.30......................... \$1A eq: Dutch gilder ................... 1.3985............. 1.3658 \$1A eq: \$ New Zealand .............. 1.2877............. 1.2659 \$1A eq: Norway kroner............... 5.2129............. 5.0657 \$1A eq: Papua NG kina............ On App.............. 1.3155 \$1A eq: Philippine peso............ On App.............. 25.729 \$1A eq: \$ Singapore................... 1.0293............. 0.9940 \$1A eq: \$ Solomons ................... 2.9599............. 2.6311 \$1A eq: Sth. Africa rand.............. 4.1083............. 4.0056 \$1A eq: Sth. Korea wan.............. 867.10......................... \$1A eq: Spain pesetas................ 105.59............. 103.12 \$1A eq: Sri Lanka r’pee ............ On App................ 39.36 \$1A eq: Sweden krona ............... 5.3905............. 5.2594 \$1A eq: Swiss franc.................... 0.9836............. 0.9611 \$1A eq: Thailand baht................... 24.19............... 21.90 \$1A eq: Vanuatu valu ................... 80.22............... 77.27 If Karla exchanges A\$400 for NZ\$, how much will she get? THINK WRITE Use the selling price in the table. The bank will sell NZ\$1.2659 for A\$1 Multiply by 400. A\$400 is worth NZ\$1.2659 × 400 Write the answer. Karla will receive NZ\$506.36 1 2 3 12WORKEDExample MQ Maths A Yr 11 - 03 Page 94 Wednesday, July 4, 2001 2:35 PM
33. 33. C h a p t e r 3 S p e n d i n g m o n e y 95 The exchange rate Use the table of exchange rates on page 94. 1 Convert A\$100 to each of the following currencies. a US dollars b UK pounds c Italian lira d French francs 2 Convert each of these amounts to Australian dollars. a 220 US dollars b 320 UK pounds c 400 EUR (Euros) d 400 000 Indonesian rupiah 3 Angie plans to visit Tokyo on business. She changes A\$800 into Japanese yen. a How much does she receive in yen? b If the trip is suddenly cancelled and she changes the yen she has back to A\$, how much will she have? c How much money has she lost because of this ‘double’ exchange? 4 Holly travels to Germany. She changes A\$660 into German marks (deutschmarks, or DM). a How many German marks does she have? b When in Germany she spends DM 480. How many marks does she have left? c If she changes these back to Australian dollars, how much will she have? 5 During an economic crisis in 1998, Indonesia experienced severe inﬂation. In one week, on Monday, A\$1 would have bought 9500 rupiah whereas on Thursday A\$1 would have bought 10 900 rupiah. On holidays in Indonesia at this time, Joel exchanged A\$120 and paid for a camera on Monday. How much would he have saved if he had waited to make the transaction on Thursday (assuming the marked price did not change). If Karla exchanges NZ\$350 for A\$ when she returns, how much will she get? THINK WRITE Use the buying price in the table. The bank will buy NZ\$1.2877 for A\$1 Divide 350 by 1.2877. NZ\$350 is worth A\$350 ÷ 1.2877 Write the answer. Karla will receive A\$271.80 1 2 3 13WORKEDExample remember 1. When you exchange A\$ for other currencies the bank sells you the other currency. Therefore: multiply by the selling price 2. When you exchange other currencies for A\$ the bank buys the other currency from you. Therefore: divide by the buying price remember 3F WORKED Example 12 WORKED Example 13 Work SHEET 3.2 MQ Maths A Yr 11 - 03 Page 95 Wednesday, July 4, 2001 2:35 PM
34. 34. 96 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d 1 What are the two types of expenses in a budget? 2 Car insurance costs \$440 per year. Write this expense as a weekly amount. 3 John’s after-tax pay is \$1800 per fortnight. Express this as a yearly amount. 4 Consider the following readings of an electricity meter: June 44 500 kWh September 47 610 kWh Calculate the electricity consumption for this quarter. 5 If credit card interest is calculated using an annual rate of 18%, what is the daily rate of interest that is charged? 6 What date is 55 days after March 10? 7 On a credit card statement, what does a ﬁgure of \$540.65 in the ‘Closing Balance’ mean? 8 When converting Australian dollars to other currency, which value should be used — buying or selling? Questions 9 and 10 refer to the following: Buy Sell Pounds sterling 0.3327 0.3127 9 Convert 25 Australian dollars to UK pounds. 10 Convert 50 UK pounds to Australian dollars. 2 MQ Maths A Yr 11 - 03 Page 96 Wednesday, July 4, 2001 4:30 PM
35. 35. C h a p t e r 3 S p e n d i n g m o n e y 97 Discount • Discount = Original price − Sale price • Percentage discount = • Sale price = Original price − percentage of the original price = (100 − percentage discount)% of the original price Proﬁt and loss • Proﬁt = Sale price − Cost price • Percentage proﬁt = • Loss = Cost price − Selling price • Percentage loss = Budgeting • A budget is a table containing an estimate of income and expenditure. • Expenses can be ﬁxed and unavoidable, or variable. • Savings can be made by reducing variable expenses. • All entries in the budget table should be calculated for the same time period as the budget itself (that is, weekly, monthly, quarterly or yearly). Credit cards • For ‘Up to 55 days interest-free period’ cards, the closing balance should be paid in full by the due date (usually 25 days from the date of the statement). Otherwise, interest is charged until the balance is repaid. • For ‘No interest-free period’ cards, interest is calculated from the date of purchase and until the balance is repaid. • The bank requires a minimum monthly payment. The amount is shown on the monthly statement. Exchange rate • The rate at which international currencies may be exchanged varies on a daily basis. • To change Australian dollars into another currency, multiply by the selling price. • To change a foreign currency into Australian dollars, divide by the buying price. summary Discount Original price --------------------------------- 100%× Profit Cost price ------------------------ 100%× Loss Cost price ------------------------ 100%× MQ Maths A Yr 11 - 03 Page 97 Wednesday, July 4, 2001 2:35 PM
36. 36. 98 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d 1 If the original price of a ‘Patches’ doll is \$40, determine its selling price after a discount of 12.5% is applied. 2 A pair of Italian-made shoes was discounted from \$180 to \$150. Calculate the percentage discount. 3 The price on a 5-piece cookware set is reduced by 15% to \$212.50. What was the price of the set before the discount? 4 Copy and complete the following table. 5 If the cost price of a microwave is \$210 and the percentage proﬁt is 22%, what is its selling price? 6 Selling a damaged rug at \$125 will incur 37.5% loss. What was the cost price of the rug? Item Cost price (\$) Percentage discount Discount (\$) Selling price (\$) a 200 12% b 150 142.50 c 98 9.80 d 16.25 113.75 e 20% 332.80 f 33 % 76 CHAPTER review 3A 3A 3A 3A 1 3 --- 3B 3B MQ Maths A Yr 11 - 03 Page 98 Wednesday, July 4, 2001 2:35 PM
37. 37. C h a p t e r 3 S p e n d i n g m o n e y 99 7 Calculate the percentage proﬁt or loss for each of the following: a a 3-piece lounge room suite: CP \$1500, SP \$2700 b a 50-mL bottle of French perfume: CP \$58, SP \$130 c last season’s dress: CP \$40, SP \$25 d a damaged toy set: CP \$18, SP \$10. 8 Rose has listed her major expenses as follows: a Prepare a weekly expenditure budget for Rose. (Put all amounts to the nearest dollar.) b Calculate the approximate amount that she can save per year if her average weekly take home pay is \$470. 9 Gas is charged at 0.6935c per megajoule (MJ) for the ﬁrst 4000 MJ used and 0.8839c per MJ thereafter. Find the cost of using 6000 MJ (to the nearest cent). Item Cost Period Rent \$434 Monthly Electricity \$130 Quarterly Gas \$60 Every 2 months Phone \$300 Quarterly Car registration \$420 Yearly Car insurance \$450 Yearly Contents insurance \$155 Yearly Health insurance \$40 Monthly Food \$100 Weekly Sport \$30 Weekly Entertainment \$20 Weekly Clothes \$120 Monthly Holidays \$1200 Yearly 3B 3C 3D MQ Maths A Yr 11 - 03 Page 99 Wednesday, July 4, 2001 2:35 PM
38. 38. 100 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d 10 An electricity bill consists of a charge for consumed electricity and the service-to-property charge. The rates for consumption are \$0.1186 for the ﬁrst 1020 kWh and \$0.125 per kWh thereafter. The service charge is constant at \$35. Calculate the total charge if the current reading of the meter shows 56 230 while the previous reading was 53 250. 11 The minimum balance owing on a credit card account is taken to be the larger of \$25 or 2.5% of the balance owing, or the excess of the closing balance over a credit limit. If the closing balance was \$1440 with a credit limit of \$1400, determine the minimum balance due. 12 An ‘up to 55 days interest-free period’ credit card was used for purchases which after the 30-day interval totalled \$1400. a Find the minimum amount due if the current credit limit on this card is \$2000 and the bank requires the largest of \$25, 2.5% of the outstanding balance or the excess above the credit limit. b If the balance was paid 10 days after the due date (which was 25 days from the statement date), what was the interest at 16% p.a. from the start of the 30-day interval? 13 Ben is in a difﬁcult situation. He needs to convert US\$100 to UK pounds and the only way this can be done is to convert the US\$ to A\$ and then change the A\$ to UK pounds. What amount will he have in UK pounds? Use the table on page 94. 3D 3E 3E testtest CHAPTER yyourselfourself testyyourselfourself 3 3F MQ Maths A Yr 11 - 03 Page 100 Monday, September 24, 2001 7:12 AM